For every twice differentiable function $$f : R \rightarrow [-2, 2]$$ with $$(f(0))^{2}+(f'(0))^{2}=85$$ which of the following statement(s) is (are) TRUE?

A

There exist r,s \in R where r<s such that 𝑓 is one-one on the open interval (r, s)

B

There exists $$X_{0} \in (-4,0)$$ such that$$\mid (f'(x_{0})) \mid \leq 1$$

C

$$\lim_{x\rightarrow\infty } f(x) =1$$

D

There exists $$\alpha$$ $$\in$$ (-4,4) such that $$f(\alpha)+f''(\alpha) = 0$$ and $$f'(\alpha) \neq 0$$